Large Scale Data Analysis - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 328

mentally as the feature family is constructed, using the same update formulas [ 1 , 13 ]
employed for the interactive aggregation during data exploration (Sect. 27.5 ). Specif-
ically, as each vertex is labeled with its branch id, the vertex's associated attributes are
added to the corresponding statistical aggregator. While this incremental approach
works well for descriptive statistics, certain attributes such as shape descriptors can-
not easily be computed in this manner, and are thus computed in a post-processing
step.

File Format We store feature families and their corresponding attributes in a modu-
lar and easily extendable file format. Typically, we save one file per feature family to
easily allow the restriction to temporal subsets, for example. At the end of each file we
store anXML-footer followed by the file offset to the start of the footer as the last eight
bytes in the file. The XML structure encodes which components are stored for the fea-
ture family, and typically comprises a simplification sequence storing the hierarchy
information in addition to a number of attributes. Any attributes stored indicate their
type in addition to meta-data such as the name of the source field, howmany bytes are
used for each value, and whether data is stored in binary or ascii format. For the sta-
tistical moments we store not only the final value, e.g. mean, but enough information
to further aggregate multiple values as needed by the parallel statistics formulas of
[ 1 , 13 ]. This requires each n -th order statistical moment to store all lower-order
moments to support aggregation. Most importantly the XML structure stores file
offsets to each corresponding block of data, allowing for the selective loading of
subsets of attributes for exploration. One immediate advantage of this file structure
is that it can be easily extended without re-writing entire files. Given a new set of
attributes, we read the XML footer, append the new data at the end of the old data
(overwriting the old footer), update the footer, and append it to the file.

27.5 Interactive Exploration of Feature-Based Statistics

One of the main advantages of our system is the ability to quickly explore a wide
variety of statistical information based on the given feature definitions. To achieve
this our framework supports four operators that map feature families, sets of features,
and statistics into new sets of features, or scalar quantities:

Definition 27.5 ( Selection )A selection S is an operator that,

given a feature family and a parameter, returns a set of features as well as (a subset)
of their corresponding attributes.

: F × R → P( F )

Note that each feature stores attribute information regarding the portion of the domain
it covers, see Fig. 27.1 a. A selection will, for most attributes, aggregate all values
in the associated subtree on-the-fly as the hierarchy is navigated. This preserves
the flexibility to base different feature families on the same set of initial attributes.
Nevertheless, if only one type of family is needed, aggregation of attributes can be
performed once and stored to accelerate the exploration, see Sect. 27.4 .